Factor Calculator
Factors (or divisors) of a number n are all integers that divide n exactly with no remainder. Prime factorization expresses n as a product of prime numbers — unique for every integer greater than 1 (Fundamental Theorem of Arithmetic).
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Tip: To find all factors: find the prime factorization first. For 12 = 2²×3: factors are 2⁰×3⁰=1, 2¹×3⁰=2, 2²×3⁰=4, 2⁰×3¹=3, 2¹×3¹=6, 2²×3¹=12. Systematic and complete.
- 1Trial division: test divisibility by 2, then odd numbers up to √n
- 2If divisible, it's a factor — add both divisor and quotient
- 3Prime factorization: keep dividing by the smallest prime factor
- 4Number of factors = product of (exponent + 1) for each prime factor
Factors of 36=1, 2, 3, 4, 6, 9, 12, 18, 3636 = 2² × 3² → (2+1)(2+1) = 9 factors
Prime factorization of 360=2³ × 3² × 5360 = 8 × 9 × 5
| Divisible by | Rule |
|---|---|
| 2 | Last digit is even (0,2,4,6,8) |
| 3 | Sum of digits divisible by 3 |
| 4 | Last 2 digits divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 9 | Sum of digits divisible by 9 |
| 10 | Last digit is 0 |
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Fun Fact
Perfect numbers equal the sum of their proper divisors: 6 = 1+2+3, 28 = 1+2+4+7+14. Only 51 perfect numbers are known. All known ones are even; whether any odd perfect numbers exist is one of the oldest unsolved problems in mathematics.
References
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